scholarly journals Impact of skull sutures, spongiform bone distribution, and aging skull conductivities on the EEG forward and inverse problems

2021 ◽  
Author(s):  
Hannah May McCann ◽  
Leandro Beltrachini
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Clinical Diagnosis ◽  
Electric Potential ◽  
Potential Distribution ◽  
Inhomogeneous Layer ◽  
Source Imaging ◽  
Bone Composition ◽  
Source Localisation ◽  
Skull Conductivity

Abstract Source imaging is a principal objective for electroencephalography (EEG), the solutions of which require forward problem (FP) computations characterising the electric potential distribution on the scalp due to known sources. Additionally, the EEG-FP is dependent upon realistic, anatomically correct volume conductors and accurate tissue conductivities, where the skull is particularly important. Skull conductivity, however, deviates according to bone composition and the presence of adult sutures. The presented study therefore analyses the effect the presence of adult sutures and differing bone composition have on the EEG-FP and inverse problem (IP) solutions. Utilising a well-established head atlas, detailed head models were generated including compact and spongiform bone and adult sutures. The true skull conductivity was considered as inhomogeneous according to spongiform bone proportion and sutures. The EEG-FP and EEG-IP were solved and compared to results employing homogeneous skull models, with varying conductivities and omitting sutures, as well as using a hypothesised aging skull conductivity model. Significant localised FP errors, with relative error up to 85%, were revealed, particularly evident along suture lines and directly related to the proportion of spongiform bone. This remained evident at various ages. Similar EEG-IP inaccuracies were found, with the largest (maximum 4.14 cm) across suture lines. It is concluded that modelling the skull as an inhomogeneous layer that varies according to spongiform bone proportion and includes differing suture conductivity is imperative for accurate EEG-FP and source localisation calculations. Their omission can result in significant errors, relevant for EEG research and clinical diagnosis.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

Variational-hemivariational inverse problem for electro-elastic unilateral frictional contact problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Othmane Baiz ◽  
Hicham Benaissa ◽  
Zakaria Faiz ◽  
Driss El Moutawakil
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Contact Problem ◽  
Existence And Uniqueness ◽  
Frictional Contact ◽  
Hemivariational Inequalities ◽  
Frictional Contact Problem ◽  
Uniqueness Of A Solution

AbstractIn the present paper, we study inverse problems for a class of nonlinear hemivariational inequalities. We prove the existence and uniqueness of a solution to inverse problems. Finally, we introduce an inverse problem for an electro-elastic frictional contact problem to illustrate our results.

scholarly journals Quantitative Observation of Electric Potential Distribution of Brittle Polyelectrolyte Hydrogels Using Microelectrode Technique

2016 ◽  
Vol 49 (8) ◽  
pp. 3100-3108 ◽  
Author(s):  
Honglei Guo ◽  
Takayuki Kurokawa ◽  
Masakazu Takahata ◽  
Wei Hong ◽  
Yoshinori Katsuyama ◽  
...  
Keyword(s):  
Electric Potential ◽  
Potential Distribution ◽  
Electric Potential Distribution ◽  
Microelectrode Technique

scholarly journals Observation of Electric Potential Distribution in Model Capacitor Sample Using Electron Holography

2012 ◽  
Vol 53 (4) ◽  
pp. 696-699 ◽  
Author(s):  
Ryuichi Kuramae ◽  
Hiroyuki Ono ◽  
Yoshinori Fujikawa ◽  
Yasukazu Murakami ◽  
Daisuke Shindo
Keyword(s):  
Electric Potential ◽  
Potential Distribution ◽  
Electron Holography ◽  
Electric Potential Distribution

scholarly journals ConvDip: A convolutional neural network for better M/EEG Source Imaging

2020 ◽  
Author(s):  
Lukas Hecker ◽  
Rebekka Rupprecht ◽  
Ludger Tebartz van Elst ◽  
Juergen Kornmeier
Keyword(s):  
Neural Network ◽  
Inverse Problem ◽  
Convolutional Neural Network ◽  
Brain Activity ◽  
Clinical Diagnostics ◽  
Dipole Model ◽  
Source Imaging ◽  
Eeg Source Imaging ◽  
Eeg Data ◽  
Inverse Solutions

AbstractEEG and MEG are well-established non-invasive methods in neuroscientific research and clinical diagnostics. Both methods provide a high temporal but low spatial resolution of brain activity. In order to gain insight about the spatial dynamics of the M/EEG one has to solve the inverse problem, which means that more than one configuration of neural sources can evoke one and the same distribution of EEG activity on the scalp. Artificial neural networks have been previously used successfully to find either one or two dipoles sources. These approaches, however, have never solved the inverse problem in a distributed dipole model with more than two dipole sources. We present ConvDip, a novel convolutional neural network (CNN) architecture that solves the EEG inverse problem in a distributed dipole model based on simulated EEG data. We show that (1) ConvDip learned to produce inverse solutions from a single time point of EEG data and (2) outperforms state-of-the-art methods (eLORETA and LCMV beamforming) on all focused performance measures. (3) It is more flexible when dealing with varying number of sources, produces less ghost sources and misses less real sources than the comparison methods. (4) It produces plausible inverse solutions for real-world EEG recordings and needs less than 40 ms for a single forward pass. Our results qualify ConvDip as an efficient and easy-to-apply novel method for source localization in EEG and MEG data, with high relevance for clinical applications, e.g. in epileptology and real time applications.

scholarly journals Adjoint Numerical Method for a Multiphysical Inverse Problem of Two-Phase Well Testing in Petroleum Reservoirs

2021 ◽  
Vol 2090 (1) ◽  
pp. 012139
Author(s):  
OA Shishkina ◽  
I M Indrupskiy
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Objective Function ◽  
Petroleum Reservoirs ◽  
Forward Problem ◽  
Adjoint Equations ◽  
Well Testing ◽  
Adjoint Methods ◽  
Two Phase ◽  
Gradient Calculation

Abstract Inverse problem solution is an integral part of data interpretation for well testing in petroleum reservoirs. In case of two-phase well tests with water injection, forward problem is based on the multiphase flow model in porous media and solved numerically. The inverse problem is based on a misfit or likelihood objective function. Adjoint methods have proved robust and efficient for gradient calculation of the objective function in this type of problems. However, if time-lapse electrical resistivity measurements during the well test are included in the objective function, both the forward and inverse problems become multiphysical, and straightforward application of the adjoint method is problematic. In this paper we present a novel adjoint algorithm for the inverse problems considered. It takes into account the structure of cross dependencies between flow and electrical equations and variables, as well as specifics of the equations (mixed parabolic-hyperbolic for flow and elliptic for electricity), numerical discretizations and grids, and measurements in the inverse problem. Decomposition is proposed for the adjoint problem which makes possible step-wise solution of the electric adjoint equations, like in the forward problem, after which a cross-term is computed and added to the right-hand side of the flow adjoint equations at this timestep. The overall procedure provides accurate gradient calculation for the multiphysical objective function while preserving robustness and efficiency of the adjoint methods. Example cases of the adjoint gradient calculation are presented and compared to straightforward difference-based gradient calculation in terms of accuracy and efficiency.

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